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Find the minimum value of the function f(x)=3^[(x^2-2)^3 +8]

Answers (1)

D Deependra Verma

Solution: We have ,

$f(x)=3^(x^2-2)^3+8$

The function $f(x)=3^phi (x)$ takes on the minimum value at the

same point as the function $phi (x)$ .

Hence ,

$phi (x)=x^6-6x^4+12x^2=x^2[(x^2-3)^2+3].$

Whence it is clear that the funtion $phi (x)$ attains the minimum value

at $x=0$ . that is why the minimum value of the function $f(x)$ is

equal to $3^0=1$

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